Question

If the zeroes of a polynomial $p(x)$ are $-3$ and $8$, then $p(x)$ equals

• A. $x^2 + 5x - 4$
• B. $(x + 3)(-x + 8)$
• C. $a(x^2 + 5x - 24)$
• D. $x^2 - 24$

Hint:

If you are unsure of the algebraic expansion, simply substitute the given zeroes into the options.
For option (B), at $x = -3$, $(x+3)(-x+8) = 0$, and at $x = 8$, $(x+3)(-x+8) = 0$.
Since both values satisfy the polynomial, it must be the correct option!

Answer 1

The Correct Option is B

Step 1: Recall what a zero means.
If $-3$ and $8$ are the zeroes of $p(x)$, then $p(-3) = 0$ and $p(8) = 0$. Instead of expanding a general product, we test each option directly at these two values.
Step 2: Test option (B), $(x+3)(-x+8)$, at both zeroes.
At $x = -3$: $(x+3) = 0$, so the whole product is $0$.
At $x = 8$: $(-x+8) = 0$, so the whole product is $0$ again. Both conditions hold.
Step 3: Confirm the other options fail.
Checking option (A) at $x=-3$: $9 - 15 - 4 = -10 \neq 0$. Checking option (D) at $x=-3$: $9-24=-15\neq0$. Option (C) has an unexplained extra letter $a$ instead of a defined constant, so it is not a clean match either. Only option (B) vanishes at both given zeroes.
\[ \boxed{p(x) = (x+3)(-x+8)} \]